The Behavior of Superconducting Thin Films in the Presence of Magnetic Fields and Currents

The general Gor’kov equation in the presence of arbitrary vector potential A(x) is solved for a superconducting thin film on the following two assumptions; 1) the ordering parameter Δ is constant all over the specimen, 2) l/ξ0 ≪1, where l is the mean free path of an electron and ξ0 the coherence length of an electron pair.It is shown that the phase transition due to magnetic field is always of the second order. The critical field is determined from the condition Δ=0.